WASHINGTON (Reuters) - The U.S. Federal Aviation Administration (FAA) will this week hold a meeting with major U.S. airlines that fly the currently grounded Boeing 737 MAX aircraft and three major pilots' unions, the agency confirmed on Thursday.

The meeting, to be held on Friday at FAA headquarters in Washington, is set for three hours and will include safety representatives from American Airlines, United Airlines and Southwest Airlines Co as well as officials from the three labour unions.

More than 300 Boeing 737 MAX jets have been grounded worldwide after nearly 350 people died in two crashes - one in Indonesia in October and another in Ethiopia last month. The FAA is also convening a joint review with aviation regulators from China, Europe, Canada, Brazil, Indonesia, Ethiopia and other countries.

American and United have cancelled flights through early June, while Southwest on Thursday announced it has cancelled flights through Aug. 5 because of the 737 MAX grounding.

Boeing has reprogrammed software on its 737 MAX passenger jet to prevent erroneous data from triggering an anti-stall system that is under mounting scrutiny following the two deadly nose-down crashes and revised pilot training.

Boeing Chief Executive Dennis Muilenburg said on Thursday that the software update is working, with about two-thirds of the fast-selling jetliner's customers having seen the fix in simulator sessions.

But on April 1, Boeing said it had delayed submitting the proposed revisions to the FAA for approval.

The FAA said the meeting is to help "the FAA to gather facts, information, and individual views to further understand their views as FAA decides what needs to be done before returning the aircraft to service."

The agency "continues to gather all available information and data in considering the return of the 737 MAX to service," it added.

Dennis Tajer, spokesman for the Allied Pilots Association that represents pilots at American Airlines, said he expected the union would be able to "provide feedback and input regarding pilot training related to the 737 MAX."

The airlines did not immediately respond to requests for comment.

Federal prosecutors aided by the FBI, the Department of Transportation's inspector general’s office and a blue-ribbon panel, are also reviewing the 737 MAX’s certification and other issues surrounding the aircraft.

U.S. lawmakers and the National Transportation Safety Board are conducting their own reviews of the FAA's certification process, which delegates some tasks to the manufacturers.

(Reporting by David Shepardson in Washington; additional reporting by Tracy Rucinski in Chicago; editing by James Dalgleish and G Crosse)